Finite Group DatabasebetaFinite Group Databasebeta| order | 14415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C961⋊C5 |
| unambiguous semidirect product | (C3×C961)⋊C5 |
| Fitting, Hall | C3×C961 ⋊ C5 |
| derived, Sylow | C961 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C961⋊C5 |
| commutator, cosocle, hypocenter | C961 | C3×C5 |
| Frattini | C31 | C3×ΓL(1,𝔽32) |
| Fitting | C3×C961 | C5 |
| socle | C3×C31 | ΓL(1,𝔽32) |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2883 |
591 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D961⋊C5, D3×C961⋊C5, C3⋊(D961⋊C5), … |
| maximal normal subgroup of | C3×D961⋊C5, D3×C961⋊C5, C3⋊(D961⋊C5), … |
| maximal quotient of | C2×C3×C961⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14415, 3);